A cyclotron is capable of accelerating protons to 100 MeV ma

A cyclotron is capable of accelerating protons to 100 MeV, maximum. (a) What are the approximate maximum kinetic energies to which deuterons and a-particles can be accelerated? (b) Compute the mass collision stopping power in water for such an cr-particle. Ignore the shell correction.

Answers: Deuteron: 50 MeV, a-particle: 101 MeV.

part b: 86 MeV cmVg.

Solution

For a particle inside cyclotron,

r_max = mv/qB

v = qBr/m

where v= velocity at exit radius r.

q= charge

B=Magnetic field magnitude

m=mass

This gives KE=1/2 m v² = q²B²r²/2m

=> KE :: q²/m

KE(deuteron)= ((1e)²/2mp )*(1mp/(1e)²) *100=50MeV

KE(alpha)= ((2e)²/4mp )*(1mp/(1e)²) *100= 100 MeV

There is no such thing as a cr-particle.